Real-time observation of the buildup of polaron in α-FAPbI3

The formation of polaron, i.e., the strong coupling process between the carrier and lattice, is considered to play a crucial role in benefiting the photoelectric performance of hybrid organic-inorganic halide perovskites. However, direct observation of the dynamical formation of polarons occurring at time scales within hundreds of femtoseconds remains a technical challenge. Here, by terahertz emission spectroscopy, we demonstrate the real-time observation of polaron formation process in FAPbI3 films. Two different polaron resonances interpreted with the anharmonic coupling emission model have been studied: P1 at ~1 THz relates to the inorganic sublattice vibration mode and the P2 at ~0.4 THz peak relates to the FA+ cation rotation mode. Moreover, P2 could be further strengthened than P1 by pumping the hot carriers to the higher sub-conduction band. Our observations could open a door for THz emission spectroscopy to be a powerful tool in studying polaron formation dynamics in perovskites.


Supporting Information
Supplementary Figure S1       ( ) = 1 2 + 2 2 + 1 4 + 2 4 + ⑵ Here, 1 is the CPGE current, 2 is mainly due to misalignment between the fast axis of the λ/4 waveplate and the incident light polarization ， and 1 and 2 are the photocurrent induced by linearly polarized light, which may be induced by linear photogalvanic effect (LPGE) or photon drag effect，D is the photocurrent generated by the photo-Dember effect. Inset in Fig. 7(f) shows the fitting parameters 1 , 2 , and D fitted from the formula (3), the parameter D is much larger than the other parameters.
Overall, the main mechanism of THz emission in HOIPs could come from the photo-Dember effect.     In OPTP measurement, the absorption peaks in the photo-induced THz conductivity are related to the intensity of phonon emission 8,9 . As shown in Fig S12, we have used photon excitation below (630nm, 1.97 eV) and above (480nm, 2.58 eV) CB2 in the optical pump-THz probe (OPTP) spectroscopy to characterize the photo-induced THz conductivity. If the observed result is mainly due to the phonon emissions generated by the cooling of hot carriers associated with the excess energy dumping, different absorption intensity at P2 should be detected using photon excitation below and above CB2. However, as shown in Fig S12, the intensities of P2 are similar. Therefore, it is incomplete to use phonon emissions generated by hot carriers cooling to explain the THz emission enhancement of P2 observed using excitation above bandgap in our study. After the substitution of MA cation in FAPbI3 (only one MA substitutes one FA in a 2 × 2 × 2 supercell, i.e., FA0.875MA0.125PbI3), the shapes of the energy curves shows that the upper conduction band of FA cations (red curve in Fig. S13(b)) shifts slightly. Hence, with the existence of MA, the transition process could be similar with the condition without MA substitution. We checked the electronic energy curves (Fig. S14) associated with the orientation of the FA molecule by DFT calculation. Fig. S14 (b-d) shows the potential energy difference (ΔE) curves of FA rotation along X, Y, and Z axis. When FA rotates or vibrates in a certain direction, the energy difference of the system is less than 0.1eV (depending on the degree of the rotation). This indicates that the orientation of FA cations does not significantly affect the total electronic energy of FAPbI3.
In the transition model, we assume that electrons are vertically excited from the VB to CB1 and CB2, where CB2 contains the energy level of the FA cations. To support this transition model, we checked the electronic energy (Fig. S14) curves and electronic structure (Fig. S13) associated with the orientation of the FA molecule. Fig. S14 (b-d) shows the potential energy difference (ΔE) curves of FA rotation along X, Y, or Z axis.
When FA rotates or vibrates in a certain direction, the energy difference of the system is less than 0.1eV (Depending on the degree of the rotation). This indicates that the orientation of FA cations does not significantly affect the total electronic energy of FAPbI3, hence, the interactions between FA and Pb-I framework are weak.
The density functional theory (DFT) calculation: The density functional theory (DFT) calculations were performed using the VASP code 10, 11 using the projectoraugmented plane wave (PAW) approach and a kinetic energy cutoff of 500 eV. The generalized gradient approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional 12 was employed to perform all calculations and Grimme's D3 13 correction was used to consider the van der Waals (vdW) interactions. The cubic-phase FAPbI3 was selected and a 2×2×2 supercell was used to model the MA doping. The potential energy curve is obtained every 10° rotation of FA. The geometry of FA was fixed, and the PbI6 inorganic frameworks and lattice constants were optimized to reproduce the symmetry lowering associated with the FA rotation and the coupling between Fa and the dynamic notions of the PbI6 framework.

THz time domain spectroscopy (THz-TDS)：Broadband
THz-TDS was carried out on the 0.95FA. The fundamental laser pulse with wavelength at 800 nm is generated by a Ti: sapphire amplifier. The fundamental laser beam was focused on ZnTe to generate THz emission. And the fundamental laser beam was modulated by an optical chopper. Measure the THz transmission signal of the resulting THz as it passes through the sample and through the substrate.

Optical pump/THz electromagnetic probe (OPTP) spectroscopy：
The OPTP system is driven by a Ti:sapphire fs amplifier laser pulse of ~35 fs duration with a repetition rate of 1 kHz. The fundamental laser pulse is divided into three beams, a pump beam, a THz generate beam, and the other beam is used as probe light to detect THz signal emitted by the sample. The pump beam was modulated by an optical chopper. A time-delay line is used to vary the optical path of the pump beam and the THz generated beam. The THz transmission signal of the sample under different time delay after optical pumping was measured.